الفهرس 
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Abstract
This thesis is mainly concerned with the nonlinear stabiiity 0.£ both
Rayleigh. Taylor and Kelvin- Helmholtz models through porous media in
the presence of different magnetic field distributions. The research examines the effects of weak viscous, Darcy’s coefficients, and streaming flows on the wave piCopagation in an interface between two uniform magnetic fluids. The two magnetic fiuids ale incompressible, ViSCOU5~ porous I uud stressed by gravity forces. Between the two fluids there exists a surface tension: An interface between two bulk media can: be observed in a. large number of technological areas: mechanical and chemical engineering , petroleum industry j and combustion. Interface dynamics plays a major role in pattern formation. It determines the shapes of objects, and therefore l it has important applications in a. wide range of interdisciplinary fields: hydrodynamics (convection patterns and shapes of boundaries between fluids ), metallurgy (dendritic shapes of crystals ), biology (medicine, biotechnology and diagnostics). The thesis is organised in four chapters as follows: Chapter one explains the fundamental aspects of the topics of reiiMI’c. h. The mainaspect is the general definition of an interface and an interfacial layer. Studies in nonlinear sta.bility theory are explained. Moreover, the technique followed in this respect such as the method of multiple scales is introduced. A review of the previous studies of both Rayleigh -Taylor and Kelvin- Helmholtz instabilities and the flow through porous media are introduced. The concepts of magnetic fluids, magnetic fluids of low visCosity and its various applications are explained. The equations
governing the motion of viscous magneue fluids through porous media and the associated boundary conditions are presented in the last section.